Week 4 Flashcards
What is Chi-squared ?
A test of difference between categorical variables (Nominal / ordinal)
Unlike binomial tests it isn’t limited to dichotomous variables (success/fail) and can test more than 2 categories
What are the two types of chi-squared tests?
1) Goodness of fit test
2) Test of association/independence
What is Benford’s law?
AKA First digit law
It states the frequency of first digits of naturally occurring numerical data such as prices or populations is likely to be small.
What are paired samples? Example?
It is data across the same group before and after intervention or under two different conditions
Example - Usually tests before and after such as whether nicotine patches help quit smoking, the two variables are the nicotine patches and whether they smoked before the test and if they smoke after.
What is a student t-test?
Difference in means of a group of measures of continuous variables (interval/ratio)
3 types of Student t-test? Which test do they correspond to?
Correspond to the tests for nominal/ordinal values
1) One sample t-test - binomial or Chi square goodness of fit
2) Independent/unpaired sample t-test - Chi-square test of association
3)Paired samples test - McNemar’s test
When is the One sample t-test used? Difference to Chi? Example?
When we want to test whether the mean of a single sample of continuous data (Interval/ratio) differs from known/hypothesised mean
It differs from chi-squared as it is not categorical data and measures means rather than frequencies/proportions
Example - Comparing 20 Male student Vo2 max tests to 20 published Vo2 max tests.
When is the Independent/unpaired samples t-test used? Difference to Chi? Example?
Compares the observed difference between the means of two independent groups
It differs as it measuring means not frequencies, of continuous (numeric) data.
Example - Comparing exam marks from Class A and Class B
When is the paired t-test used? Difference to Chi? Example?
Compares the means of two related groups / a group measure on two different occasions and the difference is compared.
Data is continuous, measures means.
Example - Comparing weight of participants before and after lockdown
What does Normality mean in terms of t-tests?
It is the assumption of normality, it is when we assume the distribution of the test results are evenly/normally distributed and shows it is accurate, it is often common with a sufficiently large sample size as it is more forgiving
What are the tests for sample t-tests?
Parametric tests - Statistical tests based on the normality assumption.
Test of normality - Should not assume normality, so use tests such as Shapiro-Will test to find a p-value to determine significance
Non Parametric tests - Don’t require the normality assumption, focuses more on order and ranking instead of face value data
Equality of variance - Using Levene’s test of EV, to test significance between two variances and whether they are equal, if not equal must do Welch’s test.
What are T-Statistics ?
What T-Tests are based off.
Similar to z-score but it is about Mean and SD of sample not population.
Equation for T Value?
Degree of freedom (df) = sample size - number of groups
Greater T value means greater difference
How is t-test data reported? Example
T value, Degree of freedom and p-value, usually with descriptive statistics such as Mean and SD.
Example - T(48) = -3.1, p = 0.003
T value with 48 degrees of freedom
-3.1 size of the difference
P = .003 = significant difference
How to calculate final report ? With example
1) Formulate hypotheses - null and alternative = (no)significant difference between two groups (group a and b exam marks)
2) Calculate means and SD
Given -
A = 78 mean, 10 SD, 25 sample size
B = 85 mean, 12 SD, 25 sample size
3) Calculate standard error and t-stats =
SE = Mean A - Mean B / Square root of (SD A^2 / sample size) = SD B^2 / sample size)
SE = 78 - 85 / square root of 10^2/25 + 12^2/25 = 3.12
T = -7 / 3.12 = 2.24
4) Calculate DF
DF = Sample A + B - 2 (groups)
5) Determine p-value
